Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
from itertools import combinations
from random import randint
from sys import stdin, stdout
from time import time

t = time()

triangles = [ k * (k+1) / 2 for k in xrange(1, int(10**5 / 2.2)) ]
triset = set(triangles)

sums = { sum(com) for com in combinations(triangles[:10**3], 2) }
yes = None

for line in stdin:
	n = int(line)
	yes = False

	if n in sums:
		stdout.write('YES\n')
		continue

	for tri in triangles:
		if n - tri in triset:
			stdout.write('YES\n')
			yes = True
			break
		elif n - tri < 0:
			break

	if not yes:
		stdout.write('NO\n')
		

#print time() - t